The sum of the divisors of $2^{5} {.3}^{7} {.5}^{3} {.7}^{2}$ is :

2^{5} {.3}^{8} {.5}^{4} {.7}^{3}

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2^{5} {.3}^{8} {.5}^{4} {.7}^{3} - 2.3.5.7

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2^{5} {.3}^{8} {.5}^{4} {.7}^{3} - 1

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none of these

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Solution

The correct option is B $2^{5} {.3}^{8} {.5}^{4} {.7}^{3} - 2.3.5.7$
Sum of divisors of ${p_{1}}^{n_{1}}, {p_{2}}^{n_{2}}, . . . . . . {p_{n}}^{n_{k}}$

$= \frac{{p_{1}}^{n_{1} + 1} - 1}{p_{1} - 1}, \frac{{p_{2}}^{n_{2} + 1} - 1}{p_{2} - 1}, . . . . . \frac{{p_{n}}^{n_{k}} - 1}{p_{n} - 1}$

Required sum is = $\frac{2^{6} - 1}{2 - 1} \times \frac{3^{8} - 1}{3 - 1} \times \frac{5^{4} - 1}{5 - 1} \times \frac{7^{3} - 1}{7 - 1}$

$= (2^{6} - 1) \times \frac{(3^{8} - 1)}{2} \times \frac{5^{4} - 1}{4} \times \frac{7^{3} - 1}{6}$

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Similar questions

Q. Simplify:
(i)

\frac{- 3}{2} + \frac{5}{4} - \frac{7}{4}

(ii)

\frac{5}{3} - \frac{7}{6} + \frac{- 2}{3}

(iii)

\frac{5}{4} - \frac{7}{6} - \frac{- 2}{3}

(iv)

\frac{- 2}{5} - \frac{- 3}{10} - \frac{- 4}{7}

(v)

\frac{5}{6} + \frac{- 2}{5} - \frac{- 2}{15}

(vi)

\frac{3}{8} - \frac{- 2}{9} + \frac{- 5}{36}

Q. Find the units digit of the expression

25^{6251} + 36^{528} + 73^{54}

Q. Calculate the range from the following data.

Marks	$26$	$38$	$54$	$65$	$72$	$88$
No. of students	$5$	$10$	$15$	$20$	$25$	$30$

The marks scored by 40 students of class IX in mathematics are given below:
$\begin{matrix} 81, & 55, & 68, & 79, & 85, & 43, & 29, & 68, & 54, & 73, & 47, 35, & 72, & 64, & 95, & 44, & 50, & 77, & 64, & 35, & 79, & 52, 45, & 54, & 70, & 83, & 62, & 64 & 72, & 92, & 84, & 76 & 63 43, & 54, & 38, & 73, & 68, & 52, & 54 \end{matrix}$
Prepare a frequency distribution with class size of 10 marks.

Q. Subtract

54 - 38

from

38 - 54

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The sum of the divisors of 25.37.53.72 is :

The correct option is B 25.38.54.73−2.3.5.7Sum of divisors of p1n1,p2n2,......pnnk=p1n1+1−1p1−1,p2n2+1−1p2−1,.....pnnk−1pn−1 Required sum is = 26−12−1×38−13−1×54−15−1×73−17−1=(26−1)×(38−1)2×54−14×73−16

The sum of the divisors of $2^{5} {.3}^{7} {.5}^{3} {.7}^{2}$ is :